es:ES, A, B:Type, Ia1, Ia2:AbsInterface(A), Ib1, Ib2:AbsInterface(B), g1:(E(Ib1)E(Ia1)),
g2:(E(Ib2)E(Ia2)).
[{Ib1}? g1 : g2]  {e:E| {[Ib1?Ib2]}(e)} E 

latex

Definitions

x:AB(x), x:A. B(x), AbsInterface(A), E(X), [f?g], {I}, f(a), {x:A| B(x)} , E, t  T, Type, ES, x:A  B(x), b, s = t, Top, Void, x:A.B(x), P  Q, <a, b>, left + right, EqDecider(T), Unit, IdLnk, Id, EOrderAxioms(E; pred?; info), EState(T), Knd, kindcase(k; a.f(a); l,t.g(l;t) ), Msg(M), type List, , , val-axiom(E;V;M;info;pred?;init;Trans;Choose;Send;val;time), e < e', r  s, , constant_function(f;A;B), P & Q, let x,y = A in B(x;y), , x.A(x), e  X, x. t(x)

Lemmas

es-E wf, p-conditional wf, subtype rel set, es-is-interface wf, assert wf, es-E-interface wf, subtype rel function, subtype rel sum, conditional wf-interface